Probability: Midwestern company

A Midwestern company that produces a particular machine component has 3 factories, one each in Chicago, Cleveland, and St. Louis. 50% of the components produced come from the Chicago factory, 20% of the components come from the Cleveland factory, and 30% of the components come from the St. Louis factory. It is known that 1.1% of the components from the Chicago factory, 1.7% of the components from the Cleveland factory, and 1.6% of the components from the St. Louis factory are defective. Given that a component is selected at random and is found to be defective, what is the probability that the component was made in Cleveland?

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